Adam, ChristophRomanczukiewicz, T.Wachla, M.Wereszczynski, Andrzej2020-05-042020-05-042018Adam, C., Romanczukiewicz, T., Wachla, M. et al. Exactly solvable gravitating perfect fluid solitons in (2 + 1) dimensions. J. High Energ. Phys. 2018, 97 (2018)1029-8479http://hdl.handle.net/10347/21990The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity is considered. We show that in an asymptotically flat space-time the model still possesses the BPS property, i.e., admits a BPS reduction to first order Bogomolnyi equations, which guarantees that the corresponding proper energy is a linear function of the topological charge. We also find the mass-radius relation as well as the maximal mass and radius. All these results are obtained in an analytical manner, which implies the complete solvability of this selfgravitating matter system. If a cosmological constant is added, then the BPS property is lost. In de Sitter (dS ) space-time both extremal and non-extremal solutions are found, where the former correspond to finite positive pressure solutions of the flat space-time model. For the asymptotic anti-de Sitter (AdS ) case, extremal solutions do not exist as there are no negative pressure BPS baby Skyrmions in flat space-time. Non-extremal solutions with AdS asymptotics do exist and may be constructed numerically. The impact of the negative cosmological constant on the mass-radius relation is studied. We also found two potentials for which exact multi-soliton solutions in the external AdS space can be obtained. Finally, we elaborate on the implications of these findings for certain three-dimensional models of holographic QCDeng© 2018 The authors. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are creditedhttps://creativecommons.org/licenses/by/4.0/Field theories in lower dimensionsSolitons monopoles and instantonsHolography and quark-gluon plasmasIntegrable field theoriesjournal article10.1007/JHEP07(2018)097open access